Coulomb blockade and cotunneling in single electron circuits with on-chip resistors: Towards the implementation of the R pump

We investigate Al single electron structures equipped with miniature (8 μm long) on-chip Cr resistors of R>Rk=h/e2≈26 kΩ. From the measurement of the Coulomb blockade in single-junction structures we evaluate the self-capacitance of our resistors per unit length, c≈62 aF/μm. We demonstrate that the cotunneling current in the transistor samples in the Coulomb blockade regime obeys the power law, I∝V3+2(R/Rk), predicted by Odintsov, Bubanja, and Schon for a transistor with pure ohmic-resistance leads. The concept of the three-junction single electron pump with on-chip resistors (R pump) is developed. We demonstrate that the technology available allows the R pump with a relative accuracy of the electron transfer of 10−8 to be implemented.